How to have zero value or a value between 200 and 400 in the output of a deep learning model?
generally the approach is to have a separate head. For example, imagine you have latent vector $z_k$, you would output two values: $h(z_k)$ and $f(z_k)$ where $0 \leq h \leq 1$ and $b_0 \leq f \leq b_1$ where $b_0$ and $b_1$ are your bounds.
In thios setup, during inference you would check $h_k$ and if its greater than some threshold (usually .5), youd evaluate/output $f_k$.
In this case your loss would look something like $L_i = L_i^{(1)}(h_i, y_i)+y_i*L_i^{(2)}(f_i,v_i)$ where $(y,v)$ are your labels, and the $L$'s are your loss of choice.